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• The tradition of problem-posing in Hungarian mathematics teaching

  233-254

  Zoltán Kovács

  Views:

  156

  Based on the literature, Pólya was influential in problem-posing research. The present paper draws attention to a book written with Pólya's collaboration, which has not yet received sufficient emphasis in the problem-posing literature. On the other hand, Pólya's impact on mathematics education in Hungary has been significant, including the problem-posing paradigm. Two works, published only in Hungarian, that rely heavily on problem-posing are highlighted. Furthermore, it is presented how problem-posing appeared in the Hungarian Complex Mathematics Teaching Experiment (1962-78) led by Tamás Varga.

  Subject Classification: 97D50

• Cultivating algorithmic thinking: an important issue for both technical and HUMAN sciences

  107-116

  Zoltán Kátai

  Lehel István Kovács

  Zoltán Kása

  Gyöngyvér Márton

  Kinga Fogarasi

  Ferenc Fogarasi

  Views:

  8

  Algorithmic thinking is a valuable skill that all people should master. In this paper we propose a one-semester, algorithm-oriented computer science course for human science students. According to our experience such an initiative could succeed only if the next recipe is followed: interesting and practical content + exciting didactical methods + minimal programming. More explicitly, we suggest: (1) A special, simple, minimal, pseudo-code like imperative programming language that integrates a graphic library. (2) Interesting, practical and problem-oriented content with philosophical implications. (3) Exciting, human science related didactical methods including art-based, inter-cultural elements.

• WMI2: interactive mathematics on the web

  393-405

  Zoltán Kovács

  Views:

  2

  After 5 years of experiments and feedback we decided to continue the software development on WebMathematics Interactive, a web-based e-learning tool, rewriting it from scratch. The demonstration version of WebMathematics Interactive 2 (WMI2) has been shown to the expert audience on the CADGME conference. In this article we summarize the development goals and results.

• Decomposition of triangles into isosceles triangles II: complete solution of the problem by using a computer

  275-300

  József Kosztolányi

  Zoltán Kovács

  Erzsébet Nagy

  Views:

  10

  We solve an open decomposition problem in elementary geometry using pure mathematics and a computer programme, utilizing a computer algebra system.

• Brute force on 10 letters

  183-193

  Zoltán Kovács

  István Hudi

  Views:

  8

  We deal with two problems in the set of 10-character-long strings. Both problems can be solved by slightly different methods, but our approach for each is brute force. As we point out, there can be differences in effectivity even in different brute force algorithms. As an additional result, we answer an open question of Raymond Smullyan's.

• Decomposition of triangles into isosceles triangles I: let the students ask bravely

  163-184

  József Kosztolányi

  Zoltán Kovács

  Erzsébet Nagy

  Views:

  8

  We report about working up an open geometric problem as a mathematical research with pupils of a mathematics camp. This paper shows the didactic aims and the methods we worked with, the didactic results. The second part of this paper gives a general solution of the problem, using pure mathematics and a computer programme.

• 14 to 18-year-old Hungarian high-school students' view of mathematicians appearing in the media - a case study

  183-194

  Orsolya Dóra Lócska

  Zoltán Kovács

  Views:

  1

  One way to develop positive attitude toward STEM subjects that popular media, including movies and films can be engaged to promote more positive and inclusive STEM images. The movie Hidden numbers offers an opportunity to explore the representations of scholars, especially mathematicians within a biographical drama. Focusing on 5 characters, this article first discusses whether these characters fit into stereotypical scientist image or not. Secondly, we examine how high school students evaluate these characters. We argue that this movie is suitable to promote positive attitude toward STEM subjects.

• Figures to the article "Assimilation of mathematical knowledge using Maple" on pages 321-331. (color plate)

  423

  Zoltán Kovács

  László Kozma

  Views:

  2

  Color plate

• Interactive web portals in mathematics

  347-361

  Róbert Vajda

  Zoltán Kovács

  Views:

  6

  Many of the recent problems in higher education (less contact seminars, the heterogeneity and the increasing number of our students) call for new instructional methods. At University of Szeged we have developed a mathematical web portal which can offer a solution for such problems among the changing circumstances. This freely available, easy-to-use web-surface supports interactive mathematical problem-solving and student self assessment. Our computer program cooperates with a lot of free software (computer algebra systems, formula parsers, converters, word processors). WebMathematics Interactive has been available for the public since June 2002 on its web page http://wmi.math.u-szeged.hu.

• On the fixed points of an affine transformation: an elementary view

  101-110

  Zoltán Kovács

  Views:

  6

  This note shows how the fixed points of an affine transformation in the plane can be constructed by an elementary geometric method. The approach presented here also shows how the affinities of the plane can be classified with the help of their fixed points.

• Assimilation of mathematical knowledge using Maple

  321-331

  Zoltán Kovács

  László Kozma

  Views:

  10

  For more than four years we have been teaching a Maple course at University of Debrecen for prospective mathematics teachers. The aim of the course is that students get some experience on mathematical visualization with Maple. At the last part of the course the student is provided with a problem of geometrical flavor. Within three or four weeks he/she must obtain a solution. In this paper we present and analyze two of student projects: rotation of the hypercube and drawing of complex functions. The concluding remark is that most of the students will profit from using Maple for such type of problems: it helps to assimilate mathematical knowledge.

• Blind versus wise use of CAS

  407-417

  Zoltán Kovács

  Views:

  1

  During my courses for mathematics major students I often use technology linked to the arising problems. In such cases I noted that some students were used to learn just some procedures, which made them able to solve (partially) some problems and when they got the result, they accepted it passively and did not relate it to the initial problem.
  In this paper I outline a strategy and investigate some simple exercises about how to develop a critical attitude towards the results obtained by technology in an introductory course to CAS.
  I believe that wise use of technology offers an effective method in teaching mathematics, without reducing the students' mental contribution.